A bipolar analog-to-digital converter (ADC) converts an analog input signal to a digital output code that can represent both positive and negative values. Although there are different ways to represent a negative number as a digital code, most representations use the most significant bit (MSB) of the code to signify whether the represented value is positive or negative. The MSB is sometimes referred to as a “sign bit”. Examples of binary representations of negative numbers include a one's complement representation and a two's complement representation.
The transfer function of an ADC is a plot of the code generated at the ADC output as function of the input signal value. Such a plot is not continuous but is a plot of 2N steps, where N the number of bits in the digital output. For an ideal ADC, a single straight line can be drawn through the points at each code-transition boundary, beginning at the origin of the plot.
FIG. 1 shows a plot 2 of an ideal transfer function 4 for a 3-bit ADC with reference points at code transition boundaries. The ADC in this example produces a total of eight steps that each represents a value of the analog input signal as a two's complement binary code. In this case, the MSB (i.e., the first bit of each code) signifies whether the code represents a negative or a positive value. For example, all of the digital codes having an MSB equal to “1” represent negative values, and all of the digital codes having an MSB equal to “0” represent either a positive value or zero. The transition occurs at one code width, which is equal to a least significant bit (LSB). The actual value of an LSB is equal to Vref/2(N−1), where Vref is the reference voltage that determines the full-scale range of the ADC (i.e., the range of analog input values that ADC can convert to digital values). The resolution of the ADC, which determines the best accuracy to which the ADC can represent an analog input value, is equal to the value of the LSB. In the example shown in FIG. 1, the resolution is Vref/4.